Common combinators in Haxe 4

combinators.hx

static final I = x -> x;
static final K = x -> y -> x;
static final A = f -> x -> f(x);
static final T = x -> f -> f(x);
static final W = f -> x -> f(x)(x);
static final C = f -> y -> x -> f(x)(y);
static final B = f -> g -> x -> f(g(x));
static final S = f -> g -> x -> f(x)(g(x));
static final P = f -> g -> x -> y -> f(g(x))(g(y));

combinators.md

Name	#	Haskell	Ramda	Sanctuary	Signature
identity	I	id	identity	I	a → a
constant	K	const	always	K	a → b → a
apply	A	($)	call	A	(a → b) → a → b
thrush	T	(&)	applyTo	T	a → (a → b) → b
duplication	W	join²	unnest²	join²	(a → a → b) → a → b
flip	C	flip	flip	flip	(a → b → c) → b → a → c
compose	B	(.), fmap²	map²	compose, map²	(b → c) → (a → b) → a → c
substitution	S	ap²	ap²	ap²	(a → b → c) → (a → b) → a → c
psi	P	on		on	(b → b → c) → (a → b) → a → a → c
fix-point¹	Y	fix			(a → a) → a

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¹) In Haxe and other non-lazy languages, it is impossible to implement the Y-combinator. Instead a variant known as the applicative or strict fix-point combinator is implemented. This variant is sometimes rererred to as the Z-combinator.

²) Algebras like ap have different implementations for different types. They work like Function combinators only for Function inputs.

references.md

Note that when I use the word "combinator" in this context, it implies "function combinator in the untyped lambda calculus".

• To Mock a Mocking Bird (book of combinatory puzzles and examples)
• Combinator Birds (summary of all combinators named by the book)
• CombinatorsJS (implementation of all the same combinators in JavaScripts)
• Fantasy Combinators (implementation of common combinators in JavaScript)
• Collected Lambdas (collection of noteworthy combinators)
• Programming With Nothing (talk)
• Church Encoding (wikipedia)
• Fixed-point combinator (wikipedia)
• Lambda calculus (wikipedia)
• SKI combinator calculus (wikipedia)
• BCKW combinator calculus (wikipedia)